Constraining nonstandard neutrino-quark interactions with solar, reactor and accelerator data

Constraining nonstandard neutrino-quark interactions with solar, reactor and accelerator data

F. J. Escrihuela Instituto de Física Corpuscular – C.S.I.C./Universitat de València
Campus de Paterna, Apt 22085, E–46071 València, Spain
   O. G. Miranda Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN
Apdo. Postal 14-740 07000 Mexico, DF, Mexico
   M. A. Tórtola II. Institut für Theoretische Physik, Universität Hamburg,
Luruper Chaussee 149, 22761 Hamburg, Germany
   J. W. F. Valle, URL: Instituto de Física Corpuscular – C.S.I.C./Universitat de València
Campus de Paterna, Apt 22085, E–46071 València, Spain

We present a reanalysis of nonstandard neutrino-down-quark interactions of electron and tau neutrinos using solar, reactor and accelerator data. In addition updating the analysis by including new solar data from SNO phase III and Borexino, as well as new KamLAND data and solar fluxes, a key role is played in our analysis by the combination of these results with the CHARM data. The latter allows us to better constrain the axial and axial-vector electron and tau-neutrino nonstandard interaction parameters characterizing the deviations from the Standard Model predictions.

preprint: IFIC/09-30

I Introduction

Current solar neutrino data Cleveland et al. (1998); Abdurashitov et al. (1990); Altmann et al. (2005); Kaether (2007); Fukuda et al. (2002); Hosaka et al. (2006); Ahmad et al. (2002a, b); Ahmed et al. (2004); Aharmim et al. (2005, 2008); Arpesella et al. (2008); Galbiati et al. (2008); Collaboration (2008), in conjunction with reactor data from the KamLAND experiment Abe et al. (2008) shows that the neutrino oscillation mechanism is the correct picture to explain the solar neutrino physics. Solar neutrino experiments are also sensitive to matter effects Wolfenstein (1978); Mikheev and Smirnov (1985), and the combination of both solar and KamLAND data determines the so called Large Mixing Angle (LMA) solution as the correct explanation to the data. For example, the LMA solution is quite robust against possible uncertainties in solar physics, such as noise density fluctuations originated by radiative zone magnetic fields Schaefer and Koonin (1987); Krastev and Smirnov (1991); Loreti and Balantekin (1994); Nunokawa et al. (1996); Burgess et al. (2004a); Burgess et al. (2003, 2004b); Fogli et al. (2007). Likewise, the LMA solution is also stable with respect to the possible existence of sizeable convective zone magnetic fields Miranda et al. (2001, 2004), that could induce spin-flavor neutrino conversions Schechter and Valle (1981); Akhmedov (1988). In all these cases, the KamLAND data play a crucial role in establishing that nonstandard effects can only play a subleading role Pakvasa and Valle (2003), their amplitude being effectively constrained.

However, while constrained by the solar and KamLAND data in an important way, neutrino nonstandard interactions (NSI) still provide an important exception to the robustness of the neutrino oscillation interpretation Friedland et al. (2004a); Guzzo et al. (2004). Indeed, it has been found that they might even shift the solution to the so–called dark side region of the neutrino parameter space Miranda et al. (2006).

Given the envisaged precision expected in upcoming oscillation studies Bandyopadhyay et al. (2007), one needs to further scrutinize the possible role of NSI Nunokawa et al. (2008). The intrinsic importance of NSI stems from the fact that they are characteristic features of theories of neutrino mass Valle (2006) and that their magnitude provides important guidance in order to distinguish the simplest high-scale seesaw models Gell-Mann et al. (1979); Yanagida (KEK lectures, 1979); Mohapatra and Senjanovic (1980); Schechter and Valle (1980, 1982) from those seesaw scenarios based at low-scale physics, such as the inverse Mohapatra and Valle (1986); Bazzocchi et al. (2009) or linear seesaw mechanisms Malinsky et al. (2005), as well as radiative models of neutrino mass Babu (1988); Zee (1980); Aristizabal Sierra et al. (2008).

In this paper we reanalyze the robustness of the oscillation interpretation of the solar neutrino data in the presence of nonstandard interactions. Besides all the solar neutrino data used in our previous study Miranda et al. (2006), here we take into account new solar data from SNO phase III Aharmim et al. (2008), the first real-time measurements of the solar Beryllium flux at Borexino Arpesella et al. (2008), as well as the new and more precise KamLAND data Abe et al. (2008). We have also considered in our calculations the new solar fluxes and uncertainties from the updated Standard Solar Model (SSM) Pena-Garay and Serenelli (2008). We show explicitly that the degenerate solution in the dark side region still remains plausible even after inclusion of these new data. Besides updating the analysis of nonstandard neutrino-down-quark interactions, we stress the key role is played by the combination of these results with the measurements of the electron-neutrino-quark cross section at the CHARM accelerator experiment. Although it is sensitive only to the interactions of electron neutrinos, when combined with solar and KamLAND data, the latter allows us to improve the determination of the tau-neutrino nonstandard axial and vector couplings

In what follows we will focus on nonstandard interactions that can be parametrized with the effective low–energy neutral currents four–fermion operator 111A recent study of CC non-standard interactions has been given in Ref. Biggio et al. (2009a). :


where P = L, R and is a first generation fermion: . The coefficients denote the strength of the NSI between the neutrinos of flavours and and the P–handed component of the fermion . For definiteness, we take for the down-type quark. However, one can also consider the presence of NSI with electrons and up and down quarks simultaneously. Current and expected limits for the case of NSI with electrons have been reported in the literature de Gouvea and Jenkins (2006); Barranco et al. (2006); Bolanos et al. (2009). Here we confine ourselves to NSI couplings involving only electron and tau neutrinos. This approximation is in principle justified in view of the somewhat stronger constraints on interactions, for a discussion see Ref. Davidson et al. (2003); Biggio et al. (2009b); Berezhiani and Rossi (2002).

Nonstandard interactions may in principle affect neutrino propagation properties in matter as well as detection cross sections and in certain cases they can also modify the assumed initial fluxes222We assume a class of models of neutrino mass where NSI leave the solar and reactor neutrino fluxes unaffected.. NSI effects in neutrino propagation affect the analysis of data from solar neutrino experiments and to some extent also KamLAND, through the vectorial NSI couplings . On the other hand detection shows sensitivity also to the axial NSI couplings in the SNO experiment. These points will be analyzed in detail in Section II, after a brief discussion of the experimental data included in our study. In Section III we will focus on the study of the non-universal nonstandard interactions, combining the results of the CHARM experiment together with our solar analysis in order to obtain a new constraint for the tau neutrino nonstandard-interaction with d-type quark. Finally we will conclude in Section IV.

Ii Sensitivity of solar and KamLAND data to NSI

Here we will adopt the simplest approximate two–neutrino picture, which is justified in view of the stringent limit on  Schwetz et al. (2008) that follows mainly from reactor neutrino experiments Apollonio et al. (1999).

ii.1 Data

In this subsection we will describe the input data required to analyze the sensitivity of solar and KamLAND neutrino data to the presence of NSI. This will include not only the experimental data samples by all the detectors considered, but also the theoretical predictions required to simulate the solar neutrino production prescribed by the SSM.

Concerning the solar neutrino data, we have included in our analysis the most recent results from the radiochemical experiments Homestake Cleveland et al. (1998), SAGE Abdurashitov et al. (1990) and GALLEX/GNO Altmann et al. (2005); Kaether (2007) , the zenith-spectra data set from Super-Kamiokande I Fukuda et al. (2002); Hosaka et al. (2006), as well as the results from the two first phases of the SNO experiment Ahmad et al. (2002a, b); Ahmed et al. (2004); Aharmim et al. (2005). The main updates with respect to our previous work Miranda et al. (2006) is the inclusion of the data from the third phase of the SNO experiment Aharmim et al. (2008), where He proportional counters have been used to measure the neutral current (NC) component of the solar neutrino flux, and the latest measurement of the Be solar neutrino rate performed by the Borexino collaboration Arpesella et al. (2008); Galbiati et al. (2008).

In our analysis we use the solar neutrino fluxes and uncertainties given by the latest version of the SSM Pena-Garay and Serenelli (2008). The latter provides an improved determination of the neutrino flux uncertainties, mainly thanks to the improved accuracy on the He-He cross section measurement and to the reduced systematic uncertainties in the determination of the surface composition of the Sun. In Ref. Pena-Garay and Serenelli (2008) two different solar model calculations are presented, corresponding to two different measurements of the solar metal abundances. For our analysis we have chosen the model corresponding to a higher solar metallicity, BPS08(GS), although we have checked that the use of the lower metallicity model BPS08(AGS) does not change our results substantially.

The KamLAND experiment observes the disappearance of reactor antineutrinos over an average distance of 180 km. Given that, in their way to the detector, reactor neutrinos can only traverse the most superficial layers of the Earth, the resulting Earth matter effects are almost negligible. The same applies also to the nonstandard interactions we are considering. However, for consistency with our analysis of solar neutrino data, in our simulation of the KamLAND experiment, we have included the effect of NSI over the antineutrino propagation. In particular, we have considered that neutrinos travel through a layer of constant matter density equal to the terrestrial crust density ( 2.6 gcm). Here we have used the latest data release from the KamLAND reactor experiment Abe et al. (2008), with a total exposure of 2881 tonyr, which brings in a big statistical improvement with respect to the previous data reported by the Collaboration Araki et al. (2005). We have restricted our analysis to the energy range above 2.6 MeV where the contributions from geo-neutrinos is less important. As we will see in the next section, the inclusion of the new KamLAND data will be very important for the improvement of the results, given the good precision achieved in the determination of the oscillation neutrino parameters.

ii.2 Effects in neutrino propagation

We first reanalyse the determination of the oscillation parameters in the presence of nonstandard interactions. The Hamiltonian describing solar neutrino evolution in the presence of NSI contains, in addition to the standard oscillations term,


a term , accounting for an effective potential induced by the NSI with matter, which may be written as:


Here and are two effective parameters that, according to the current bounds discussed above (), are related with the vectorial couplings which affect the neutrino propagation by333 For the derivation of the effective couplings in the general three-neutrino framework see Ref.Guzzo et al. (2002).:


The quantity in Eq. (3) is the number density of the down-type quark along the neutrino path, and is the atmospheric neutrino mixing angle.

From Eqs. (2) and (3) one sees that the solar neutrino mixing angle in the presence of nonstandard interactions is given by the following expression:




Therefore, and as discussed in Ref.Miranda et al. (2006), there exists a degeneracy between the non-universal coupling and the neutrino mixing angle which makes possible to explain the solar neutrino data for values of the vacuum mixing angle in the dark side (), for large enough values of :


For instance, for the typical values of the solar neutrino energies and matter densities one has . Indeed, as we showed in Miranda et al. (2006), the effect of NSI on solar neutrino propagation implies the presence of an additional LMA-D solution whose status we now reanalyse in the light of new data.

We now turn to the combined solar + KamLAND analysis. Following the considerations above, we have performed a new analysis of all the solar neutrino data discussed in Section II.1 combined with the recent KamLAND result Abe et al. (2008).

Figure 1: The left-bottom panel indicates 90%, 95% and 99% C.L. allowed region from the solar and solar + KamLAND combined analysis, the result of which is presented as a zoom in the top-right panel, where the shaded regions show the result of the current analysis while the lines indicate the earlier regions Miranda et al. (2006) for comparison. One sees that the dark side solution is still allowed in the presence of nonstandard interactions. The other two panels indicate the corresponding projections. In all cases, we marginalize over the NSI parameters and .

The main result is shown in Fig. 1. There, we plot the allowed regions (90, 95 and 99 % C.L.) in the solar neutrino oscillation parameter space () obtained in the analysis of solar and solar + KamLAND neutrino data, after marginalizing over the NSI parameters in our 4-dimensional analysis: (, , , ). The profiles as a function of each parameter are also shown. One can see that the region in the so-called dark side of the neutrino parameters Miranda et al. (2006) remains even after the inclusion of the new data. Note however that its status is somewhat worse than previously. In contrast, as seen in the figure, the other solutions LMA-0 and LMA-II Miranda et al. (2006) which were present before have disappeared as a result of the new KamLAND data, that now provide a very precise measurement of .

Figure 2: Neutrino survival probabilities averaged over the B neutrino production region for three reference points (see text for details). Lines are compared with the experimental rates for the pp neutrino flux (from the combination of all solar experiments), the 0.862 MeV Be line (from Borexino) and two estimated values of the B neutrino flux from Borexino and SNO (third phase). Here, vertical error bars correspond to the experimental errors, while the horizontal ones indicate the energy range observed at the experiment.

In order to better understand the results obtained, we plot at Fig. 2 the neutrino survival probabilities for different reference points. First we have considered the global best fit point from the combined solar + KamLAND analysis, labeled as ”global best fit” in the figure, with the following parameter values: (, , , ) = (0.32, 7.9 10 eV, -0.15, -0.10). We have also considered the best fit point in the absence of NSI: (0.30, 7.9 10 eV, 0.00 ,0.00), labeled as ”BF without NSI”, and allowed with a = 2.7, and finally the best fit point in the “dark side” of the oscillation parameters (labeled as ”BF dark side”) with (0.70, 7.9 10 eV, -0.15, 0.95) and = 2.9. As we see all points are in perfect agreement with the low energy (pp and Be) measurements. Concerning the most energetic boron neutrinos, where matter effects are more important, and as a result there is a higher NSI–sensitivity of the corresponding profiles, the presence of NSI provides an slightly better agreement with the data than the standard one without NSI, mainly thanks to the flatter spectrum predicted above 5 MeV. The “dark-side” solution also gives predictions for the survival probability of boron neutrinos which are compatible with the experimental results. From the different predictions obtained for these 3 reference points above a few MeV, one sees that this region could be crucial in order to break the degeneracy among the various solutions. Therefore, a better measurement of the boron neutrino flux with a lower threshold (like the ones expected from Super-K-III and SNO Takeuchi (2008); Klein (July 2009)) will be of great help. On the other hand, a very precise measurement of the pep and beryllium neutrino fluxes may also contribute to lift the degeneracy between the standard and dark-side solutions.

Figure 3: Bounds on and from the combined analysis of Solar plus KamLAND neutrino data. One sees that the parameter is now constrained to only one region while for the case of there are two possible regions, one corresponding to the standard light side solution and the other one (less favored) to the so called dark side region.

By analysing the goodness of the neutrino oscillation solutions in the presence of NSI one can also constrain the NSI parameters and . In order to do this we first marginalize our 4-parameter analysis with respect to the remaining three neutrino parameters. The results are shown in Fig. 3. One can see that the new data allow us to constraint , the flavor changing parameter, while for the flavor conserving case there is still room for relatively large values of that correspond to the solution in the dark side of the neutrino oscillation parameters. These are the bounds we obtained at the 90% C.L.


The above limits are in good agreement with the forecast made in Fig. 3 of Miranda et al. (2006), assuming the best possible determination of the neutrino mixing parameters due to KamLAND . In fact, they are even a bit better than expected from the improvement of KamLAND data only. The reason for this is the subsequent improvement of solar data, which slightly improved their sensitivity to the nonstandard interactions.

For the flavour-changing effective coupling , one can use the first expression in Eq. (4) to translate the bound obtained in Eq. (8) into a limit over the vectorial coupling :


where we have used the best fit value for the atmospheric mixing angle Schwetz et al. (2008). So far, the strongest limit on this parameter is Davidson et al. (2003). From our analysis, we see that solar neutrino data are not only sensitive to the sign of this coupling but also we have improved the lower bound.

ii.3 Effects in neutrino detection

The presence of nonstandard interactions can also affect the detection processes at some experiments. In particular, the cross section for the neutral current detection reaction at SNO:


is proportional to , where is the coupling of the neutrino current to the axial isovector hadronic current Bahcall et al. (1988). Therefore, the presence of an axial nonstandard coupling would give rise to an extra contribution to the NC signal at the SNO experiment. This nonstandard contribution can be parametrised in the following way Davidson et al. (2003):


where terms of order have been neglected. Here denotes the boron neutrino flux, and the effective axial coupling is defined as in Davidson et al. (2003):


once the nonstandard axial couplings with up-type quarks are set to zero. Note that , denoting the couplings entering in the effective Lagrangian shown in Eq. (1). Thus, is independent of the effective couplings and defined in Eq. (4). So far we have assumed in our analysis that . This assumption is well justified due to the good agreement between the SNO NC measurement: =  (stat)  (syst) Aharmim et al. (2008) and the SSM prediction for the boron flux = Pena-Garay and Serenelli (2008). However, we now relax this assumption by including the effect of the new parameter .

Figure 4: The shaded regions in the left panel show the updated analysis of all solar neutrino data combined with recent KamLAND results in the presence of the axial NSI coupling. The lines show, for comparison, the updated regions obtained only with the vector NSI couplings. We show in the right panel the profile with respect to the axial NSI parameter obtained using all solar neutrino data combined with KamLAND . One sees how the data prefer .

The results obtained in a generalized 5-parameter-analysis which takes into account the presence of a non-zero axial component of the NSI are summarized in Fig. 4. In the left panel we compare the allowed regions at 90, 95 and 99% C.L. obtained in the full 5-parameter-analysis (filled/colored regions) with the ones obtained in the previous section, neglecting the effect of the axial NSI couplings (hollow lines). One sees that both analysis are consistent, though, as expected, the inclusion of the axial parameter in the analysis somewhat extends the allowed region. In the right panel we show the profile as a function of the effective axial coupling . There, one sees that the neutrino data clearly prefers , thanks to the good agreement between the predicted boron neutrino flux and the NC observations at SNO, as stated above. We obtain we following allowed range at 90% C.L.


Using Eq. (13), the above bound on the effective axial coupling can be translated into individual bounds on the NSI parameters . Since we are neglecting the nonstandard interactions of the muon neutrino, this formula depends only on the probabilities , and on the NSI couplings and . From the recent values for the average probabilities reported by SNO Aharmim et al. (2008):


one gets an allowed region in the parameter space (, ), represented (at the 90% C.L.) as a diagonal band in Fig. 6 in the next section. There, it will used combined with neutrino laboratory data to obtain improved constraints on the neutrino NSI couplings.

Iii Constraints on non-universal NSI

In addition of solar+ KamLAND, laboratory experiments measuring neutrino-nucleon scattering show sensitivity to neutrino non-standard interactions on d-type-quarks. In particular, here we will combine the results of the accelerator experiment CHARM together with the ones in Sec. II in order to obtain stronger constraints on the NSI parameters. Given the sensitivity of the considered experiments to different NSI parameters, we have been forced to simplify the analyses reducing the number of parameters by focusing on the flavour-conserving non-universal nonstandard couplings. Within this approximation, the parameters relevant for each experiment are shown in Table 1.

Solar propagation
Solar NC detection
KamLAND propagation
CHARM detection
Table 1: Sensitivity of neutrino experiments to flavor conserving NSI parameters

iii.1 Charm

We now turn to the analysis of CHARM data. CHARM was an accelerator experiment measuring the ratio of the neutral current to the charge current cross section for electron (anti)neutrinos off quarks. We have used the results reported by the CHARM experiment for the cross section. In particular the experiment measured the relation Dorenbosch et al. (1986),


The most general expression for including all types of NSI parameters is given by


Here we are interested in the flavor conserving -type quark interaction. Then, we will neglect all flavor-changing nonstandard contributions, implying that , as well as nonstandard couplings to the -type quark, so that . In this case our simplified expression for Eqs. (17) and (18) would be


Then, we can compute the for the CHARM data:


where and are defined by the result given in Eq. (16).

The constraints in the (, ) plane at 68, 90, 95 and 99% C.L. obtained from this analysis are shown in Fig. 5.

Figure 5: Constraints at 68, 90, 95 and 99% C.L. on the neutrino NSI couplings and from CHARM data.

iii.2 Combined analysis

Figure 6: Constraints on the vector (left) and axial-vector (right) NSI couplings from our global analysis at 90, 95 and 99% C.L., and from the separate solar plus KamLAND and CHARM data sets (dashed lines).
vectorial couplings
one parameter at a time
axial couplings
one parameter at a time
Table 2: New constraints on the vectorial and axial NSI couplings at 90% C.L. obtained from the analysis of CHARM data alone and from our global analysis combining CHARM with solar and KamLAND results.

In the previous sections we have discussed the sensitivity of solar experiments, KamLAND and CHARM to the nonstandard interactions separately. In this subsection we exploit the complementarity of the information we can get from the different experiments by combining CHARM data with our previous results from the analysis of the solar and KamLAND data. This enables us to obtain stronger constraints on the NSI couplings.

The regions for the vector (left) and axial-vector (right) NSI couplings allowed by the global analysis are given in Fig. 6, where they are also compared with the constraints coming only from the CHARM data and that from the solar plus KamLAND data. First, the bounds obtained from the analysis of CHARM data and shown in Fig. 5, have been translated into two independent bounds on and (see vertical bands in Fig. 6). The regions allowed by the solar+KamLAND combination (diagonal bands in the figure) have been derived from the bounds on the non-universal nonstandard neutrino interactions obtained in Sec. II. In particular, the limits on the vectorial couplings and come from the allowed values for the effective coupling in Eq. (8), after using the definition of of Eq. (4) and the 1 allowed region for the atmospheric mixing angle  Schwetz et al. (2008). Note the existence of two allowed islands, in correspondence with the two allowed regions of neutrino oscillation parameters in the presence of NSI (see upper-right panel at Fig. 1). The lower one corresponds to the usual LMA solution, while the upper island comes from the solution in the dark side. On the other hand, using the average probabilities in Eq. (15) we have reanalysed the results obtained for the effective axial coupling in Eq. (14). This results in a constraint for the axial couplings and . From the two panels of Fig. 6 one sees that, as expected, there is a degeneracy in the determination of the two vectorial and axial parameters from solar and KamLAND data only. After the combination with CHARM we break this degeneracy and obtain the allowed regions shown in color at Fig. 6.

In Table 2 we quote the 90% C.L. allowed intervals for the couplings , , and arising from the combined analysis, as taken directly from Fig. 6. In order to compare with previous bounds obtained in a one-parameter-at-a-time analysis Davidson et al. (2003), we also present the results obtained following that approach in our analysis of CHARM data alone and in the global analysis including solar and KamLAND data as well. In this case, we see how the combination with solar and KamLAND data improves significantly the existing bounds on the electron-neutrino NSI couplings, obtained using CHARM data only Davidson et al. (2003). Now, concerning the tau-neutrino NSI couplings, we have improved the existing bounds derived from the invisible decay width measurement of the Z from LEP data: , Davidson et al. (2003).

Iv Conclusions

We have updated the solar neutrino analysis for the case of NSI of neutrinos with d-type quark by including new solar data from SNO phase III and Borexino, as well as new KamLAND data and updated solar fluxes. We have found that the additional dark-side of neutrino parameter space found in Ref. Miranda et al. (2006) still survives, while the previous LMA-0 and LMA-II which were present before have now disappeared as a result of the new data. The issue arises of how to lift this degeneracy in future studies. First we note that, since KamLAND is basically insensitive to matter effects, it will not help in resolving the degeneracy, as explicitly verified in Fig. 3 of Ref. Miranda et al. (2006). Next comes improved solar neutrino data. The form of the expected neutrino survival probability shown in Fig. 2 suggests that the best region to discriminate the degenerate solution from the normal one is the intermediate energy solar neutrino region, where the relevant experiments are Borexino Arpesella et al. (2008); Galbiati et al. (2008); Collaboration (2008) and KamLAND-solar Nakamura (2004), as well as the low energy threshold analysis expected from Super-K-III and SNO Takeuchi (2008); Klein (July 2009).

Further information relevant to lift the degeneracy may come from atmospheric and laboratory data. Indeed the LMA-D solution induced by non-standard interactions of neutrinos with quarks may become inconsistent with atmospheric and laboratory data Miranda et al. (2006); Friedland et al. (2004b). As noted in Ref. Miranda et al. (2006) currently it is not. Should the situation change with improved data we note that still the degeneracy will not disappear since the NSI couplings may affect not only down-type quark species but also up-type quarks and/or electrons. The analysis in this case would introduce new parameters. Therefore, we conclude that the neutrino oscillation interpretation of solar neutrino data is still fragile with respect to the presence of nonstandard interactions.

In summary, we have studied the limits on the non-standard interaction couplings , , , and from present neutrino data. Thanks to the combination of solar and KamLAD neutrino data with the results from the CHARM experiment, we have given improved bounds on the vector and axial NSI couplings involving electron and tau neutrino interactions on down-type quarks.


Work supported by Spanish grants FPA2008-00319/FPA and PROMETEO/2009/091. OGM was supported by CONACyT-Mexico and SNI. M.A.T. is supported by the DFG (Germany) under grant SFB-676. FJE thanks Cinvestav for hospitality when part of this work was performed.


  • Cleveland et al. (1998) B. T. Cleveland et al., Astrophys. J. 496, 505 (1998).
  • Abdurashitov et al. (1990) J. N. Abdurashitov et al. (SAGE), Phys. Rev. C80, 015807 (1990), eprint 0901.2200.
  • Altmann et al. (2005) M. Altmann et al. (GNO), Phys. Lett. B616, 174 (2005), eprint hep-ex/0504037.
  • Kaether (2007) F. Kaether (2007), eprint Heidelberg, 2007. [].
  • Fukuda et al. (2002) S. Fukuda et al. (Super-Kamiokande collaboration), Phys. Lett. B539, 179 (2002), eprint hep-ex/0205075.
  • Hosaka et al. (2006) J. Hosaka et al. (Super-Kamkiokande), Phys. Rev. D73, 112001 (2006), eprint hep-ex/0508053.
  • Ahmad et al. (2002a) Q. R. Ahmad et al. (SNO collaboration), Phys. Rev. Lett. 89, 011301 (2002a), eprint nucl-ex/0204008.
  • Ahmad et al. (2002b) Q. R. Ahmad et al. (SNO collaboration), Phys. Rev. Lett. 89, 011302 (2002b), eprint nucl-ex/0204009.
  • Ahmed et al. (2004) S. N. Ahmed et al. (SNO), Phys. Rev. Lett. 92, 181301 (2004), eprint nucl-ex/0309004.
  • Aharmim et al. (2005) B. Aharmim et al. (SNO), Phys. Rev. C72, 055502 (2005), eprint nucl-ex/0502021.
  • Aharmim et al. (2008) B. Aharmim et al. (SNO), Phys. Rev. Lett. 101, 111301 (2008), eprint 0806.0989.
  • Arpesella et al. (2008) C. Arpesella et al. (The Borexino), Phys. Rev. Lett. 101, 091302 (2008), eprint 0805.3843.
  • Galbiati et al. (2008) C. Galbiati et al., J. Phys. Conf. Ser. 136, 022001 (2008).
  • Collaboration (2008) T. B. Collaboration (2008), eprint 0808.2868.
  • Abe et al. (2008) S. Abe et al. (KamLAND), Phys. Rev. Lett. 100, 221803 (2008), eprint 0801.4589.
  • Wolfenstein (1978) L. Wolfenstein, Phys. Rev. D17, 2369 (1978).
  • Mikheev and Smirnov (1985) S. P. Mikheev and A. Y. Smirnov, Sov. J. Nucl. Phys. 42, 913 (1985).
  • Schaefer and Koonin (1987) A. Schaefer and S. E. Koonin, Phys. Lett. B185, 417 (1987).
  • Krastev and Smirnov (1991) P. I. Krastev and A. Y. Smirnov, Mod. Phys. Lett. A6, 1001 (1991).
  • Loreti and Balantekin (1994) F. N. Loreti and A. B. Balantekin, Phys. Rev. D50, 4762 (1994), eprint nucl-th/9406003.
  • Nunokawa et al. (1996) H. Nunokawa, A. Rossi, V. B. Semikoz, and J. W. F. Valle, Nucl. Phys. B472, 495 (1996), eprint hep-ph/9602307.
  • Burgess et al. (2004a) C. P. Burgess, N. S. Dzhalilov, T. I. Rashba, V. B. Semikoz, and J. W. F. Valle, Mon. Not. Roy. Astron. Soc. 348, 609 (2004a), eprint astro-ph/0304462.
  • Burgess et al. (2003) C. Burgess et al., Astrophys. J. 588, L65 (2003), eprint hep-ph/0209094.
  • Burgess et al. (2004b) C. P. Burgess et al., JCAP 0401, 007 (2004b), eprint hep-ph/0310366.
  • Fogli et al. (2007) G. L. Fogli, E. Lisi, A. Marrone, D. Montanino, and A. Palazzo, Phys. Rev. D76, 033006 (2007), eprint 0704.2568.
  • Miranda et al. (2001) O. G. Miranda et al., Nucl. Phys. B595, 360 (2001), eprint hep-ph/0005259.
  • Miranda et al. (2004) O. G. Miranda, T. I. Rashba, A. I. Rez, and J. W. F. Valle, Phys. Rev. Lett. 93, 051304 (2004), eprint hep-ph/0311014.
  • Schechter and Valle (1981) J. Schechter and J. W. F. Valle, Phys. Rev. D24, 1883 (1981), err. D25, 283 (1982).
  • Akhmedov (1988) E. K. Akhmedov, Phys. Lett. B213, 64 (1988).
  • Pakvasa and Valle (2003) S. Pakvasa and J. W. F. Valle (2003), proc. of the Indian National Academy of Sciences on Neutrinos, Vol. 70A, No.1, p.189 - 222 (2004), Eds. D. Indumathi, M.V.N. Murthy and G. Rajasekaran, eprint hep-ph/0301061.
  • Friedland et al. (2004a) A. Friedland, C. Lunardini, and C. Pena-Garay, Phys. Lett. B594, 347 (2004a), eprint hep-ph/0402266.
  • Guzzo et al. (2004) M. M. Guzzo, P. C. de Holanda, and O. L. G. Peres, Phys. Lett. B591, 1 (2004), eprint hep-ph/0403134.
  • Miranda et al. (2006) O. G. Miranda, M. A. Tortola, and J. W. F. Valle, JHEP 10, 008 (2006), eprint hep-ph/0406280.
  • Bandyopadhyay et al. (2007) A. Bandyopadhyay et al. (ISS Physics Working Group) (2007), eprint arXiv:0710.4947 [hep-ph].
  • Nunokawa et al. (2008) H. Nunokawa, S. J. Parke, and J. W. F. Valle, Prog. Part. Nucl. Phys. 60, 338 (2008), eprint arXiv:0710.0554 [hep-ph].
  • Valle (2006) J. W. F. Valle, J. Phys. Conf. Ser. 53, 473 (2006), review based on lectures at the Corfu Summer Institute on Elementary Particle Physics in September 2005, eprint hep-ph/0608101.
  • Gell-Mann et al. (1979) M. Gell-Mann, P. Ramond, and R. Slansky (1979), print-80-0576 (CERN).
  • Yanagida (KEK lectures, 1979) T. Yanagida (KEK lectures, 1979), ed. Sawada and Sugamoto (KEK, 1979).
  • Mohapatra and Senjanovic (1980) R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 91 (1980).
  • Schechter and Valle (1980) J. Schechter and J. W. F. Valle, Phys. Rev. D22, 2227 (1980).
  • Schechter and Valle (1982) J. Schechter and J. W. F. Valle, Phys. Rev. D25, 774 (1982).
  • Mohapatra and Valle (1986) R. N. Mohapatra and J. W. F. Valle, Phys. Rev. D34, 1642 (1986).
  • Bazzocchi et al. (2009) F. Bazzocchi, D. G. Cerdeno, C. Munoz, and J. W. F. Valle (2009), eprint 0907.1262.
  • Malinsky et al. (2005) M. Malinsky, J. C. Romao, and J. W. F. Valle, Phys. Rev. Lett. 95, 161801 (2005), eprint hep-ph/0506296.
  • Babu (1988) K. S. Babu, Phys. Lett. B203, 132 (1988).
  • Zee (1980) A. Zee, Phys. Lett. B93, 389 (1980).
  • Aristizabal Sierra et al. (2008) D. Aristizabal Sierra, M. Hirsch, and S. G. Kovalenko, Phys. Rev. D77, 055011 (2008), eprint 0710.5699.
  • Pena-Garay and Serenelli (2008) C. Pena-Garay and A. Serenelli (2008), eprint 0811.2424.
  • Biggio et al. (2009a) C. Biggio, M. Blennow, and E. Fernandez-Martinez (2009a), eprint 0907.0097.
  • de Gouvea and Jenkins (2006) A. de Gouvea and J. Jenkins, Phys. Rev. D74, 033004 (2006), eprint hep-ph/0603036.
  • Barranco et al. (2006) J. Barranco, O. G. Miranda, C. A. Moura, and J. W. F. Valle, Phys. Rev. D73, 113001 (2006), eprint hep-ph/0512195.
  • Bolanos et al. (2009) A. Bolanos, O. G. Miranda, A. Palazzo, M. A. Tortola, and J. W. F. Valle, Phys. Rev. D79, 113012 (2009), eprint 0812.4417.
  • Davidson et al. (2003) S. Davidson, C. Pena-Garay, N. Rius, and A. Santamaria, JHEP 03, 011 (2003), eprint hep-ph/0302093.
  • Biggio et al. (2009b) C. Biggio, M. Blennow, and E. Fernandez-Martinez, JHEP 03, 139 (2009b), eprint 0902.0607.
  • Berezhiani and Rossi (2002) Z. Berezhiani and A. Rossi, Phys. Lett. B535, 207 (2002), eprint hep-ph/0111137.
  • Schwetz et al. (2008) T. Schwetz, M. Tortola, and J. W. F. Valle, New J. Phys. 10, 113011 (2008), eprint 0808.2016.
  • Apollonio et al. (1999) M. Apollonio et al. (CHOOZ collaboration), Phys. Lett. B466, 415 (1999), eprint hep-ex/9907037.
  • Araki et al. (2005) T. Araki et al. (KamLAND collaboration), Phys. Rev. Lett. 94, 081801 (2005).
  • Guzzo et al. (2002) M. Guzzo et al., Nucl. Phys. B629, 479 (2002), eprint hep-ph/0112310 v3 KamLAND-updated version.
  • Takeuchi (2008) Y. Takeuchi, J. Phys. Conf. Ser. 120, 052008 (2008).
  • Klein (July 2009) J. Klein (SNO) (July 2009), Talk presented at “TAUP 2009”.
  • Bahcall et al. (1988) J. N. Bahcall, K. Kubodera, and S. Nozawa, Phys. Rev. D38, 1030 (1988).
  • Dorenbosch et al. (1986) J. Dorenbosch et al. (CHARM), Phys. Lett. B180, 303 (1986).
  • Nakamura (2004) K. Nakamura (KamLAND), AIP Conf. Proc. 721, 12 (2004).
  • Friedland et al. (2004b) A. Friedland, C. Lunardini, and M. Maltoni, Phys. Rev. D70, 111301 (2004b), eprint hep-ph/0408264.
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